Radio-frequency local area network (LAN) systems are highly regulated by the federal government. For example, the frequency bands of approximately 5.15-5.25 GHz, 5.25-5.35 GHz, and 5.725-5.825 GHz unlicensed national information structure (U-NII) bands are regulated by Title 47, Section 15.407 of the United States Code of Federal Regulations (CFR). While the CFR specifies certain limitations on the use of radio-frequency networks, other standards committees, such as the Institute of Electrical and Electronics Engineers (IEEE), specify technical requirements for wireless systems to ensure cross-compatibility of wireless systems from different manufacturers. For example, the IEEE “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications: High-Speed Physical Layer in the 5 GHz Band” (hereinafter “the IEEE 5 GHz standard”) provides several requirements for systems operating in the 5 GHz band.
One of the requirements set forth in the IEEE 5 GHz standard is an OFDM physical layer convergence procedure (PLCP) sub-layer. Specifically, FIG. 1A shows a Presentation Protocol Data Unit (PPDU) frame in the IEEE 5 GHz standard. As shown in FIG. 1A, the PPDU frame includes a short-training period 110, a long-training period 120 following the short-training period 110, a signaling period 130 following the long-training period 120, and a plurality of data periods 140, 142, 144 that follow the signaling period 130. The long-training period 120, the signaling period 130, and the plurality of data periods 140, 142, 144 include a guard interval (GI) as defined in the IEEE 5 GHz standard.
The short-training period 110 contains ten symbols (e.g., t1, t2 . . . t9, t10), which are used for signal detecting, coarse-frequency acquisition, diversity selection, and other functions as defined by the IEEE 5 GHz standard. Since the short-training period 110 is described in detail in the IEEE 5 GHz standard, further discussion of the short-training period 110 is omitted here.
The long-training period 120 contains a guard interval (GI2) and two long-training symbols, T1 and T2. As specified in the IEEE 5 GHz standard, each of the long-training symbol T1 and T2 consists of 53 sub-carriers including a zero value at DC, which are modulated by elements of sequence X, given by:
                    X        =                              {                          1              ,              1              ,                              -                1                            ,                              -                1                            ,              1              ,              1              ,                              -                1                            ,              1              ,                              -                1                            ,              1              ,              1              ,              1              ,              1              ,              1              ,              1              ,                              -                1                            ,                              -                1                            ,              1              ,              1              ,                              -                1                            ,              1              ,              1              ,              1              ,              1              ,              0              ,              1              ,                              -                1                            ,                              -                1                            ,              1              ,              1              ,                              -                1                            ,              1              ,                              -                1                            ,              1              ,                              -                1                            ,                              -                1                            ,                              -                1                            ,                              -                1                            ,                              -                1                            ,              1              ,              1              ,                              -                1                            ,                              -                1                            ,              1              ,                              -                1                            ,              1              ,                              -                1                            ,              1              ,              1              ,              1              ,              1                        }                    .                                    [                  Eq          .                                          ⁢          1                ]            Additionally, the IEEE 5 GHz standard requires that the long-training symbols be generated according to:
                                          x            ⁡                          (              t              )                                =                                    w              ⁡                              (                t                )                                      ⁢                                          ∑                                  k                  =                  0                                53                            ⁢                                                          ⁢                                                X                  ⁡                                      (                    k                    )                                                  ⁢                                  ⅇ                                                            j2π                      ⁡                                              (                                                  k                          -                          26                                                )                                                              ⁢                                                                  Δ                        F                                            ⁡                                              (                                                  t                          -                                                      T                                                          G                              ⁢                                                                                                                          ⁢                              12                                                                                                      )                                                                                                                                ,                            [                  Eq          .                                          ⁢          2                ]            where x(t) is a time-domain representation of the long training symbol; w(t) is a weighting factor for the purpose of spectral shaping; k is a sub-carrier index; X(k) is a coefficient of the training symbol as defined by Eq. 1; and TG/2 is the guard interval, which is defined by the IEEE 5 GHz standard as 1.6 μs.
In addition to specifying the content of the long-training symbols according to Eq. 2, the IEEE 5 GHz standard further requires that the number of long-training symbols be two (e.g., T1 and T2), thereby improving the accuracy of channel estimation.
The IEEE 5 GHz standard further dictates that the first long training symbol T1 be identical to the second long training symbol T2. Thus, designating the identical long-training symbols as X, the first long-training symbol X 155 and the second long-training symbol X 165 are transmitted consecutively during the long-training period 120. Hence, for a two-branch transmitter-diversity OFDM system as shown in FIG. 2, a first transmitter 260 transmits:                (1) two long-training symbols X 155a and X 165a across a first channel HA during the long-training period 120;        (2) signaling information S 170a across the first channel HA during the signaling period 130; and        (3) data D1 180a and D2 190a across the first channel HA for subsequent data periods 140, 142.        
Similarly, a second transmitter 265 transmits:                (1) two long-training symbols X 155b and X 165b across a second channel HB during the long-training period 120;        (2) signaling information S 170b across the second channel HB during the signaling period 130; and        (3) data D1 180b and D2 190b across the second channel HB for subsequent data periods 140, 142.        
The transmitted signals are received at a receiver 205 as a function of the transmitted symbol and the channel characteristics. After removing the guard interval, each received symbol is inverse Fourier transformed. Thus, for a two-branch transmitter-diversity OFDM system as shown in FIG. 2, the received frequency domain signals Y1 may be represented as:Y1=(HA·X)+(H9·X)+Z1  [Eq. 3].where Z1 represents the received noise, the channel characteristics HA and HB are presumed to be time-invariant during the frame duration, and the propagation delay over these two channels are presumed to be substantially the same. Since the same long-training symbol X is transmitted from both branches of the two-branch transmitter-diversity system, Eq. 3 simplifies to:Y1=(HA+HB)·X+Z2  [Eq. 4].Similarly, the subsequent received data blocks are represented by:Y2=(HA+HB)·X+Z2  [Eq. 5],Y3=(HA+HB)·S+Z3  [Eq. 6],Y4=HA·DAI+HB·DBI+Z4  [Eq. 7],and:Y5=HA·DA2+HB·DB2+Z5  [Eq. 8].
Eqs. 4 and 5, in the aggregate, result in:(Y1+Y2)·X*=(HA+HB)(2|X|2)+(Z1+Z2)·X*  [Eq. 9],which may be re-written as:
                                          H            A                    +                      H            B                          =                                                            (                                                      Y                    1                                    +                                      Y                    2                                                  )                            ·              X                        2                    -                                    (                                                Z                  1                                +                                  Z                  2                                            )                        2                                                          or, more specifically, as:
                                                                        H                A                            ⁡                              (                k                )                                      +                                          H                B                            ⁡                              (                k                )                                              =                                                                      (                                                                                    Y                        1                                            ⁡                                              (                        k                        )                                                              +                                                                  Y                        2                                            ⁡                                              (                        k                        )                                                                              )                                ·                                  X                  ⁡                                      (                    k                    )                                                              2                        -                                          (                                                                            Z                      1                                        ⁡                                          (                      k                      )                                                        +                                                            Z                      2                                        ⁡                                          (                      k                      )                                                                      )                            2                                      ,                  k          =          1                ,        ⋯        ⁢                                  ,        N        ,                            [                  Eq          .                                          ⁢          10                ]            where N represents the number of OFDM sub-carriers, and k represents the sub-carrier index
Since, as shown in Eq. 1, X(k)∈{±1} for all k, the complex coefficient X*(k) of the transmitted symbol X(k) will be equal to the transmitted symbol X(k). Furthermore, since X(k)∈{±1}, the square norm |X(k)|2 of the transmitted symbol X(k) will be 1. Additionally, since X(k)∈{±1}, the statistics of (Z1(k)+Z2(k))X(k), without loss of generality, is the same as that of (Z1(k)+Z2(k)).
By omitting the noise terms, the aggregate effect of both channels HC=HA+HB can be estimated by:
                                                        H              C                        ⁡                          (              k              )                                ≈                                                    (                                                                            Y                      1                                        ⁡                                          (                      k                      )                                                        +                                                            Y                      2                                        ⁡                                          (                      k                      )                                                                      )                            ·                              X                ⁡                                  (                  k                  )                                                      2                          ,                  k          =          1                ,        ⋯        ⁢                                  ,        N        ,                            [                  Eq          .                                          ⁢          11                ]            
While Eq. 11 provides an avenue for calculating the combined channel characteristics for HC, it is evident that the duplicative transmission of X provides very little assistance in distinguishing channel characteristics of the individual channels HA and HB. In other words, because two branches HA and HB are used for transmitting a single X, a classic one-equation two-unknown system is presented in which only the aggregate characteristics HC may be calculated to any degree of certainty. Furthermore, while the duplicative transmission of X increases the signal-to-noise ratio (SNR), the increase in SNR provides little help in resolving the characteristics of each individual channel.
Although complex algorithms exist to segregate the individual channel effects from the aggregate channel effect, these algorithms make additional presumptions about the channels in order to properly estimate the characteristics of each channel. Thus, these channel estimation algorithms are only as good as their initial presumptions. Furthermore, due to the complexity of these channel estimation algorithms, when the two-branch transmitter-diversity system is expanded to multiple-branches (e.g., three-branch, four-branch, etc.), the complexity of calculations increases exponentially.
Thus, a heretofore-unaddressed need exists in the industry to address the aforementioned deficiencies and inadequacies.